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ON THE CONNECTEDNESS OF THE BRANCH LOCI OF NON-ORIENTABLE UNBORDERED KLEIN SURFACES OF LOW GENUS

Published online by Cambridge University Press:  22 December 2014

E. BUJALANCE
Affiliation:
Departamento de Matemáticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040-Madrid, Spain e-mail: ebujalance@mat.uned.es
J. J. ETAYO
Affiliation:
Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense, 28040-Madrid, Spain e-mail: jetayo@mat.ucm.es
E. MARTÍNEZ
Affiliation:
Departamento de Matemáticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040-Madrid, Spain e-mail: emartinez@mat.uned.es
B. SZEPIETOWSKI
Affiliation:
Institute of Mathematics, University of Gdańsk. Ul. Wita, Stwosza 57, 80-952 Gdańsk, Poland e-mail: blaszep@mat.ug.edu.pl
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Abstract

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This paper is devoted to determine the connectedness of the branch loci of the moduli space of non-orientable unbordered Klein surfaces. We obtain a result similar to Nielsen's in order to determine topological conjugacy of automorphisms of prime order on such surfaces. Using this result we prove that the branch locus is connected for surfaces of topological genus 4 and 5.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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